# Multiband full-bandwidth anisotropic Eliashberg theory of interfacial electron-phonon coupling and high-T$_c$ superconductivity in FeSe/SrTiO$_3$

## TL;DR

This paper develops a detailed multiband anisotropic Eliashberg theory to understand how interfacial phonons influence high-temperature superconductivity in FeSe/SrTiO$_3$, explaining experimental features and predicting spectral signatures.

## Contribution

It introduces a material-specific, multiband, full bandwidth Eliashberg framework to analyze interfacial electron-phonon interactions in FeSe/SrTiO$_3$, revealing their role in high T$_c$ superconductivity.

## Key findings

- Interfacial electron-phonon coupling significantly contributes to high T$_c$ despite weak coupling constant.
- Replica bands decrease T$_c$, but deep Fermi-sea pairing enhances it.
- Predicted a strong-coupling dip-hump feature in tunneling spectra.

## Abstract

We examine the impact of interfacial phonons on the superconducting state of FeSe/SrTiO$_3$ developing a material's specific multiband, full bandwidth, and anisotropic Eliashberg theory for this system. Our self-consistent calculations highlight the importance of the interfacial electron-phonon interaction, which is hidden behind the seemingly weak-coupling constant {\lambda}$_m$ = 0.4, in mediating the high T$_c$, and explain other puzzling experimental observations, such as the s-wave symmetry and replica bands. We discover that the formation of replica bands has a T$_c$ decreasing effect that is nevertheless compensated by deep Fermi-sea Cooper pairing which has a T$_c$ enhancing effect. We predict a strong-coupling dip-hump signature in the tunneling spectra due to the interfacial coupling.